The generator matrix

 1  0  0  0  1  1  1  1  2  1  X  1 X+2  1  2  1  1  1  1  2 X+2  1  1  1  1  1  2  2  X
 0  1  0  0  0  1  2  3  1 X+2  0 X+1  1  1  1  2  3 X+1  3  1  1  X X+2  0  X X+1  1  1  2
 0  0  1  0  0  1  3  2  3  1  1  3  X X+2  1  3 X+1  2  0 X+2  0  0 X+3  X X+2  2  1  X  1
 0  0  0  1  1  2  1  3  3  0 X+3  3 X+3 X+2  X  X  1  0  3 X+3  2 X+2  0  0 X+3 X+3  X  X  3
 0  0  0  0  X  0  0  0  0 X+2  X  X  X X+2 X+2  2  2  2 X+2  X X+2  X  X X+2  2 X+2  X  2  2

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+230x^23+489x^24+1082x^25+1156x^26+2018x^27+1911x^28+2558x^29+1988x^30+2068x^31+1198x^32+1008x^33+366x^34+226x^35+49x^36+22x^37+8x^38+2x^39+2x^41+2x^42

The gray image is a code over GF(2) with n=116, k=14 and d=46.
This code was found by Heurico 1.16 in 7.97 seconds.